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Appendix III.




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P. 510. Proof that normal to contact passes through
meet of pitch lines.—In Fig. 884, let A and B be centres of
rotation, and c the common normal to tooth surface,------a con-

tinuous straight line because the surfaces are tangential.
c and D be centres of curvature.

Also let

Now, for a very small motion we may substitute a quadric
chain A c B D for the wheels, where A c and B D are cranks, and
c D a coupling rod; for the curved surfaces at E are merely parts
of huge link pins having c and D for centres respectively. There-
fore, for any one instant the angular velocities of wheels and
cranks are identical.

Now, angular velocities of wheels AB are inversely as pitch
circle radii, or as B G : A G. And angular velocities of links A
and B are inversely as the divisions of the fixed link made by the
coupler (see pp. 863-4) or as BF : A F. Hence BG = BF and
A G = A F : the points G and F must coincide: and the normal
c D must pass through the meet G.

P. 554. Electric Transmission : further notes.

Units. — Electric energy is now estimated by the product
of E.M.F. (volts) and Current (amperes): the resulting units
being watts. Thus :

But H,R

Energy in watts —EC

ft. Ibs. per m.

and Electrical H.P. =    ~

.'. Foot pounds per m. — E C x 45 -4